SummaryThe receiver operating characteristic (ROC) curve is used to evaluate a biomarker's ability for classifying disease status. The Youden Index (J), the maximum potential effectiveness of a biomarker, is a common summary measure of the ROC curve. In biomarker development, levels may be unquantifiable below a limit of detection (LOD) and missing from the overall dataset. Disregarding these observations may negatively bias the ROC curve and thus J. Several correction methods have been suggested for mean estimation and testing; however, little has been written about the ROC curve or its summary measures. We adapt non-parametric (empirical) and semi-parametric (ROC-GLM [generalized linear model]) methods and propose parametric methods (maximum likelihood (ML)) to estimate J and the optimal cut-point (c*) for a biomarker affected by a LOD. We develop unbiased estimators of J and c* via ML for normally and gamma distributed biomarkers. Alpha level confidence intervals are proposed using delta and bootstrap methods for the ML, semi-parametric, and non-parametric approaches respectively. Simulation studies are conducted over a range of distributional scenarios and sample sizes evaluating estimators' bias, root-mean square error, and coverage probability; the average bias was less than one percent for ML and GLM methods across scenarios and decreases with increased sample size. An example using polychlorinated biphenyl levels to classify women with and without endometriosis illustrates the potential benefits of these methods. We address the limitations and usefulness of each method in order to give researchers guidance in constructing appropriate estimates of biomarkers' true discriminating capabilities.
The literature on exposure to lipophilic agents such as polychlorinated biphenyls (PCBs) is conflicting, posing challenges for the interpretation of potential human health risks. Laboratory variation in quantifying PCBs may account for some of the conflicting study results. For example, for quantification purposes, blood is often used as a proxy for adipose tissue, which makes it necessary to model serum lipids when assessing health risks of PCBs. Using a simulation study, we evaluated four statistical models (unadjusted, standardized, adjusted, and two-stage) for the analysis of PCB exposure, serum lipids, and health outcome risk (breast cancer). We applied eight candidate true causal scenarios, depicted by directed acyclic graphs, to illustrate the ramifications of misspecification of underlying assumptions when interpreting results. Statistical models that deviated from underlying causal assumptions generated biased results. Lipid standardization, or the division of serum concentrations by serum lipids, was observed to be highly prone to bias. We conclude that investigators must consider biology, biologic medium (e.g., nonfasting blood samples), laboratory measurement, and other underlying modeling assumptions when devising a statistical plan for assessing health outcomes in relation to environmental exposures.
Biomarker use in exposure assessment is increasingly common, and consideration of related issues is of growing importance. Exposure quantification may be compromised when measurement is subject to a lower threshold. Statistical modeling of such data requires a decision regarding the handling of such readings. Various authors have considered this problem. In the context of linear regression analysis, Richardson and Ciampi (Am J Epidemiol 2003;157:355-63) proposed replacement of data below a threshold by a constant equal to the expectation for such data to yield unbiased estimates. Use of such an imputation has some limitations; distributional assumptions are required, and bias reduction in estimation of regression parameters is asymptotic, thereby presenting concerns about small studies. In this paper, the authors propose distribution-free methods for managing values below detection limits and evaluate the biases that may result when exposure measurement is constrained by a lower threshold. The authors utilize an analytical approach and a simulation study to assess the effects of the proposed replacement method on estimates. These results may inform decisions regarding analytical plans for future studies and provide a possible explanation for some amount of the discordance seen in extant literature.
The results from this meta-analysis suggest that physical activity in pregnancy provides a slight protective effect against the development of GDM. Studies evaluating type, timing, duration, and compliance of physical activity regimens are warranted to best inform obstetric guidelines.
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